A hybrid Chelyshkov wavelet-finite differences method for time-fractional black-Scholes equation
Publish place: Journal of Mahani Mathematical Research، Vol: 13، Issue: 2
Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_KJMMRC-13-2_027
تاریخ نمایه سازی: 30 مرداد 1403
Abstract:
In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization. A second order finite difference formula is used to time discretization and space discretization is done by a spectral method based on Chelyshkov wavelets and an operational process by defining Chelyshkov wavelets operational matrices. Convergence and error analysis for Chelyshkov wavelets approximation and also for the proposed method are discussed. The method is validated and its accuracy, convergency and efficiency are demonstrated through some cases with given accurate solutions. The method is also utilize for pricing various European options conducted by a time-fractional Black-Scholes model
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Authors
Seyyed Amjad Samareh Hashemi
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Habibollah Saeedi
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Ali Foroush Bastani
Department of Mathematics, Institute for Advanced Studies in Basic Sciences, P.O. Box ۴۵۱۹۵-۱۱۵۹, Zanjan, Iran
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